部分填充手征等离子体波导的电磁波

 把麦克斯韦方程和电磁场分解成横向和纵向分量, 导出了简明的一般性的手征等离子体填充的任意截面波导的波动方程和横向纵向场的关系式。对于部分填充手征等离子体波导, 导出了它的色散方程。这一方程的数值解给出了HE₁₁, EH₀₁和HE₂₁模式的色散图。随着手征等离子体填充面积的增大, EH₀₁模式的色散曲线向更高的频率移动。随着手征导纳的增加, 传播常数减小。     

The ultraviolet behaviour of integrable quantum field theories,affine Toda field theory

We investigate the thermodynamic Bethe ansatz (TBA) equations for a system of particles which dynamically interacts via the scattering matrix of affine Toda field theory and whose statistical interaction is of a general Haldane type. Up to the first leading order, we provide general approximated analytical expressions for the solutions of these equations from which we derive general formulae for the ultraviolet scaling functions for theories in which the underlying Lie algebra is simply laced. For several explicit models we compare the quality of the approximated analytical solutions against the numerical solutions. We address the question of existence and uniqueness of the solutions of the TBA equations, derive precise error estimates and determine the rate of convergence for the applied numerical procedure. A general expression for the Fourier transformed kernels of the TBA equations allows one to derive the related Y-systems and a reformulation of the equations into a universal form.     

Dynamically orthogonal field equations for continuous stochastic dynamical systems

In this work we derive an exact, closed set of evolution equations for general continuous stochastic fields described by a Stochastic Partial Differential Equation (SPDE). By hypothesizing a decomposition of the solution field into a mean and stochastic dynamical component, we derive a system of field equations consisting of a Partial Differential Equation (PDE) for the mean field, a family of PDEs for the orthonormal basis that describe the stochastic subspace where the stochasticity ‘lives’ as well as a system of Stochastic Differential Equations that defines how the stochasticity evolves in the time varying stochastic subspace. These new evolution equations are derived directly from the original SPDE, using nothing more than a dynamically orthogonal condition on the representation of the solution. If additional restrictions are assumed on the form of the representation, we recover both the Proper Orthogonal Decomposition equations and the generalized Polynomial Chaos equations. We apply this novel methodology to two cases of two-dimensional viscous fluid flows described by the Navier–Stokes equations and we compare our results with Monte Carlo simulations.     

Phantom energy mediates a long-range repulsive force

Scalar field models with nonstandard kinetic terms have been proposed in the context of k inflation, of Born-Infeld Lagrangians, of phantom energy and, more in general, of low-energy string theory. In general, scalar fields are expected to couple to matter inducing a new interaction. In this Letter I derive the cosmological perturbation equations and the Yukawa correction to gravity for such general models. I find three interesting results: first, when the field behaves as phantom energy (equation of state less than -1), then the coupling strength is negative, inducing a long-range repulsive force; second, the dark-energy field might cluster on astrophysical scales; third, applying the formalism to a Brans-Dicke theory with a general kinetic term it is shown that its Newtonian effects depend on a single parameter that generalizes the Brans-Dicke constant.     

Constraint equations for general hypersurfaces and applications to shells

Hypersurfaces of arbitrary causal character embedded in a spacetime are studied with the aim of extracting necessary and sufficient free data on the submanifold suitable for reconstructing the spacetime metric and its first derivative along the hypersurface. The constraint equations for hypersurfaces of arbitrary causal character are then computed explicitly in terms of this hypersurface data, thus providing a framework capable of unifying, and extending, the standard constraint equations in the spacelike and in the characteristic cases to the general situation. This may have interesting applications in well-posedness problems more general than those already treated in the literature. As a simple application of the constraint equations for general hypersurfaces, we derive the field equations for shells of matter when no restriction whatsoever on the causal character of the shell is imposed.     

Nonlinear dynamics in a Fabry-Perot resonator

We develop a general formalism to describe the dynamical behavior of an ensemble of two-level systems in a Fabry-Perot cavity. Our main result is a set of space and time-dependent, integro-differential equations for the slowly varying radiation and atomic variables, which we derive through a precise analysis of the slowly-varying amplitude approximation in the presence of counter-propagating fields. With the help of new and properly chosen variables we recast these equations in a form that makes their boundary conditions formally identical to those of an ideal Fabry-Perot resonator, and introduce in a natural way a modal structure even for systems with arbitrary mirror reflectivity. We derive simplified forms of these equations in the uniform field limit and within the more general single-frequency approximation. Finally, we extend our formulation to include driven systems such as optically bistable devices and the laser with an injected signal.     

String field equations from the generalized sigma model II

We improve and extend a method introduced in an earlier paper for deriving string field equations. The idea is to impose conformal invariance on a generalized sigma model, using a background field method that ensures covariance under very general non-local coordinate transformations. The method is used to derive the free string equations, as well as the interacting equations for the graviton-dilaton system. The full interacting string field equations derived by this method should be manifestly background independent.     

Lovelock gravity from entropic force

In this paper, we first generalize the formulation of entropic gravity to ( $n+1$ )-dimensional spacetime and derive Newton’s law of gravity and Friedmann equation in arbitrary dimensions. Then, we extend the discussion to higher order gravity theories and propose an entropic origin for Gauss–Bonnet gravity and more general Lovelock gravity in arbitrary dimensions. As a result, we are able to derive Newton’s law of gravitation as well as the corresponding Friedmann equations in these gravity theories. This procedure naturally leads to a derivation of the higher dimensional gravitational coupling constant of Friedmann/Einstein equation which is in complete agreement with the results obtained by comparing the weak field limit of Einstein equation with Poisson equation in higher dimensions. Our strategy is to start from first principles and assuming the entropy associated with the apparent horizon given by the expression previously known via black hole thermodynamics, but replacing the horizon radius $r_+$ with the apparent horizon radius $R$ . Our study shows that the approach presented here is powerful enough to derive the gravitational field equations in any gravity theory and further supports the viability of Verlinde’s proposal.     

The evolution of longitudinal and transverse acoustic waves in a medium with paramagnetic impurities

We study the bipartial interaction of longitudinal and transverse acoustic pulses with a system of paramagnetic impurities with an effective spin S=1/2 in a crystalline layer or on a surface in the presence of an arbitrarily directed external constant magnetic field. We derive a new system of evolution equations that describes this interaction and show that, in the absence of losses, for equal phase velocities of these acoustic components, and under the condition of their unidirectional propagation, the original system reduces to a new integrable system of equations. The derived integrable system describes the pulse dynamics outside the scope of the slow-envelope approximation. For one of the reductions of the general model that corresponds to the new integrable model, we give the corresponding equations of the inverse scattering transform method and find soliton solutions. We investigate the dynamics and formation conditions of the phonon avalanche that arises when the initial completely or incompletely inverted state of the spin system decays. We discuss the application of our results to describing the interaction dynamics of spins and acoustic pulses in various systems with an external magnetic field.     

Landau electron in a rotating environment: A general factorization of time evolution

For the Landau problem with a rotating magnetic field and a confining potential in the (changing) direction of the field, we derive a general factorization of the time evolution operator that includes the adiabatic factorization as a special case. The confining potential is assumed to be of a general form and it can correspond to nonlinear Heisenberg equations of motion. The rotation operator associated with the solid angle Berry phase is used to transform the problem to a rotating reference frame. In the rotating reference frame, we derive a natural factorization of the time evolution operator by recognizing the crucial role played by a gauge transformation. The major complexity of the problem arises from the coupling between motion in the direction of the magnetic field and motion perpendicular to the field. In the factorization, this complexity is consolidated into a single operator which approaches the identity operator when the potential confines the particle sufficiently close to a rotating plane perpendicular to the magnetic field. The structure of this operator is clarified by deriving an expression for its generating Hamiltonian. The adiabatic limit and non-adiabatic effects follow as consequences of the general factorization which are clarified using the magnetic translation concept.     

Error Estimates of Mixed Methods for Optimal Control Problems Governed by General Elliptic Equations

In this paper, we investigate the error estimates of mixed finite element methods for optimal control problems governed by general elliptic equations. The state and co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control variable is approximated by piecewise constant functions. We derive $L^2$ and $H^{-1}$-error estimates both for the control variable and the state variables. Finally, a numerical example is given to demonstrate the theoretical results.     

Phantom damping of matter perturbations

Cosmological scaling solutions are particularly important in solving the coincidence problem of dark energy. We derive the equations of sub-Hubble linear matter perturbations for a general scalar-field Lagrangian—including quintessence, tachyon, dilatonic ghost condensate and k-essence—and solve them analytically for scaling solutions. We find that matter perturbations are always damped if a phantom field is coupled to dark matter and identify the cases in which the gravitational potential is constant. This provides an interesting possibility to place stringent observational constraints on scaling dark energy models.     

Quantum Statistical Aspects of Interactions Between the Radiation Field and Two Entangled Two-Level Atoms in the Presence of Stark Shift Terms

We consider a system consisting of two two-level atoms interacting with a radiation field, including Stark shift terms, and investigate the effect of Stark shift terms on the interaction between the radiation field and the two atoms. Within the framework of the Heisenberg picture, we obtain the general solution to the operator equations of motion. In addition, we derive the general solution obtained by solving the system of differential equations. Some statistical aspects such as atomic inversion and linear entropy are discussed in detail. We study the effect of the time-dependent function on the population inversion and linear entropy. Finally, we examine the linear entropy, concurrence, and quantum and classical correlations for different values of the detuning parameter.     

Electrostatic and magnetostatic solutions in a Lorentz-violating electrodynamics model

We propose an effective Lorentz-violating electrodynamics model via the static de Sitter metric, which is deviated from the Minkowski metric by a minuscule amount depending on the cosmological constant. We obtain the electromagnetic field equations via the vierbein decomposition of the tensors. In addition, as an application of the electromagnetic field equations obtained, we derive the solutions of the electrostatic field and the magnetostatic field due to a point charge and a circle current, respectively, and discuss the implication of the effect of Lorentz violation in our electromagnetic theory.PACS 04.20.Cv; 04.40.-b; 98.80.Jk; 11.30.Cp     

Dimensional crossover driven by an electric field

We study the steady-state dynamics of the Hubbard model driven out of equilibrium by a constant electric field and coupled to a dissipative heat bath. For a very strong field, we find a dimensional reduction: the system behaves as an equilibrium Hubbard model in lower dimensions. We derive steady-state equations for the dynamical mean-field theory in the presence of dissipation. We discuss how the electric field induced dimensional crossover affects the momentum resolved and integrated spectral functions, the energy distribution function, as well as the steady current in the nonlinear regime.     

Some Anisotropic Universes in the Presence of Imperfect Fluid Coupling with Spatial Curvature

We consider Bianchi VI spacetime, which also can be reduced to Bianchi types VI₀-V-III-I. We initially consider the most general form of the energy-momentum tensor which yields anisotropic stress and heat flow. We then derive an energy-momentum tensor that couples with the spatial curvature in a way so as to cancel out the terms that arise due to the spatial curvature in the evolution equations of the Einstein field equations. We obtain exact solutions for the universes indefinitely expanding with constant mean deceleration parameter. The solutions are beriefly discussed for each Bianchi type. The dynamics of the models and fluid are examined briefly, and the models that can approach to isotropy are determined. We conclude that even if the observed universe is almost isotropic, this does not necessarily imply the isotropy of the fluid (e.g., dark energy) affecting the evolution of the universe within the context of general relativity.     

Model of line preserving field line motions using Euler potentials

We consider behavior of finite magnetic field lines during reconnection processes. We portray field line motions using Euler potentials representation. Here, we propose a new insight into plasma flow fields related with magnetic reconnection. In this approach reconnection is treated as a breakage of magnetic topology, which results in deviation from the line preserving flow regime. We derive constraints and the general equations for these flows. In our approach the flux preserving flows are treated as a special case of line preserving regime. We also derive a constraint on a non-ideal term in Ohm’s Law within diffusion regions, which relates plasma flow with resistivity, and which must hold for non-reconnective diffusion. We also propose a new method of detecting magnetic reconnection.     

Topologically massive planar universes with constant twist

We derive the general from of the topologically massive Einstein equations for stationary metrics. It is found that all these metrics have a nonvanishing twist. We then provide the complete set of solutions with constant twist and show their isometries.     

Derivation of Smoluchowski equations with corrections for Fokker-Planck and BGK collision models

The time evolution of the phase space distribution function for a classical particle in contact with a heat bath and in an external force field can be described by a kinetic equation. From this starting point, for either Fokker-Planck or BGK (Bhatnagar-Gross-Krook) collision models, we derive, with a projection operator technique, Smoluchowski equations for the configuration space density with corrections in reciprocal powers of the friction constant. For the Fokker-Planck model our results in Laplace space agree with Brinkman, and in the time domain, with Wilemski and Titulaer. For the BGK model, we find that the leading term is the familiar Smoluchowski equation, but the first correction term differs from the Fokker-Planck case primarily by the inclusion of a fourth order space derivative or super Burnett term. Finally, from the corrected Smoluchowski equations for both collision models, in the spirit of Kramers, we calculate the escape rate over a barrier to fifth order in the reciprocal friction constant, for a particle initially in a potential well.